Algebra II
A.93 Honors
Test Practice
TEST is TUESDAY, FEB 26
Monday, February 25
1) Match each Standard Form equation to the conic section it represents:
a) y  a( x  h)  k P1
2
d)
( x  h) 2 ( y  k ) 2

 1 E2
b2
a2
C1.
E1.
E2.
P1.
H1.
H2.
b) ( x  h)  ( y  k )  r C1
2
e)
2
2
( x  h) 2 ( y  k ) 2

 1 H1
a2
b2
( x  h) 2 ( y  k ) 2
c)

 1 E1
a2
b2
f)
( y  k ) 2 ( x  h) 2

 1 H2
a2
b2
circle with center (h, k) and radius r
ellipse with center (h, k) and a horizontal major axis
ellipse with center (h, k) and a vertical major axis
parabola with vertex (h, k) and axis of symmetry x = h
horizontal hyperbola with center (h,k)
vertical hyperbola with center (h,k)
Parabolas- Find the vertex and axis of symmetry for each and graph (use 5 accurate points):
2) y  2 x 2
Vertex __ (0, 0) _____
Axis of symmetry _x=0 (y-axis)______
See graphs at end of document
3) y  ( x  7)2  4
Vertex _ ( 7, 4) ______
Axis of symmetry __ x  7 _____
See graphs at end of document
LOOK CAREFULLY AT SCALES FOR EACH GRAPH!
1
4) y  ( x  1) 2  3 dotted line, shade inside curve
2
Vertex __ (1,3) _____
5) y  3( x  2)2  5 solid line, shade outside
Vertex _ (2, 5) ______ (below) curve
Axis of symmetry _ x  1 ______
Axis of symmetry ___ x  2 ____
See graphs at end of document
See graphs at end of document
Change each to standard form by completing the square; then state its vertex and axis of symmetry.
6) y  x 2  8x  9
7) f ( x)  3x 2  12 x  2
y  ( x  4) 2  25
vertex : (4, 25)
axis : x  4
f ( x)  3( x  2) 2  14
vertex : (2, 14)
axis : x  2
8) f ( x)  2 x 2  24 x  10
f ( x)  2( x  6) 2  82
vertex : (6,82)
axis : x  6
Distance and Midpoint:
9) Distance is always a _positive__ number.
10) Give the distance formula:
d  ( x2  x1 )2  ( y2  y1 )2
Find the distance between each of the following points:
11) (3, 7) and (0, 2)
d  34
12) (0,3 6) and (5, 6)
d 7
13) (5, 7) and (5, 2)
d 5 5
Find the midpoint between each of the following points:
14) (3, 7) and (0, 2)
 3 9 
M  , 
2 2 
15) (1,8) and (5,12)
M   2,10
16) (3 7, 7) and ( 7, 2)
9

M   2 7, 
2

Circles: find the center and radius for each and graph:
17) ( x  2)2  ( y  4)2  25
Center _ ( 2, 4) ______
Radius ___5____
18) ( x  6)2  y 2  4
Center ___ ( 6, 0) ____
Radius ___2____
See graphs at end of document
See graphs at end of document
Change each to standard form by completing the square; then state its center and radius.
19) x 2  10 x  y 2  13
20) x 2  12 x  y 2  6 y  4  0
( x  5) 2  y 2  38
center ( 5, 0)
( x  6) 2  ( y  3) 2  49
center (6,3)
r7
r  38
Ellipses:
( x  1)2 ( y  2) 2

1
21)
25
16
horizontal or vertical?
center _____ (1, 2) ____
length of major axis __10_____
length of minor axis ____8___
c 2  9 c  3 _____
foci (1  3, 2)  (2, 2) (4, 2)
Graph:
22)
( x  3) 2 ( y  1) 2

1
9
25
horizontal or vertical?
center __ ( 3,1) _______
length of major axis __10_____
length of minor axis ____6___
c 2  16 c  4 ________
foci (3,1  4)  (3,5) (3, 3) __
Graph:
Endpoints of major axis: (4, -2)
(-6, -2)
Endpoints of major axis: (-3, 6)
(-3, -4)
Endpoints of minor axis
(-1, -6)
Endpoints of minor axis
(0, 1)
(-1, 2)
Center (-1, -2)
Center (-3, 1)
Foci: (2, -2) & (-4, -2)
Foci: (-3, 5) & (-3, -3)
(-6, 1)
Hyperbolas:
( x  1)2 ( y  2) 2
23)

1
25
16
horizontal or vertical?
center ___ (1, 2) ______
foci (1  41, 2)
Graph:
24)
( y  3) 2 ( x  1) 2

1
9
25
horizontal or vertical?
center __ (1, 3) _______
foci (1, 3  34)
Graph:
Mixture of Writing Equations: (use the graphs to help if necessary)
25) Write an equation for a parabola with vertex (5, 1) that is of “normal” size and opens down.
y  ( x  5)2  1
26) Write an equation for a parabola that is very narrow, opens up, shifted right 3 and up 5.
y  3( x  3)2  5 (lead coeff must be  1)
27) Write an equation for a circle with center at the origin and a radius of
x2  y 2  3
28) Write an equation for a circle with center (9, 2) and radius = 4.
( x  9)2  ( y  2)2  16
29) Write an equation of a circle tangent to the y-axis with center (6, 5).
( x  6)2  ( y  5)2  36
3.
30) Write an equation of an ellipse with center at (3,8) , length of minor axis is 6, and foci at
(2,8) and (8,8) .
( x  3) 2 ( y  8) 2

1
34
9
31) Write an equation of an ellipse whose major axis has
endpoints (2,8) and (2, 0) and whose foci are (2, 7) and (2,1) .
( x  2) 2 ( y  4) 2

1
7
16
32) Change to standard form and identify the type of conic section: 6 x 2  5 y 2  36 x  40 y  104  0
( x  3)2 ( y  4) 2

 1 ellipse
5
6
33) Write an equation of a vertical hyperbola with center at (1, 4) , vertices at (1, 7) and (1,1) ,
3
and the slope of the asymptotes = 
5
2
2
( y  4) ( x  1)

1
9
25
34) Write an equation of a hyperbola with vertices at (2, 6) and (4, 6) and whose foci are
(6, 6) and (8, 6) .
( x  1) 2 ( y  6) 2

1
9
40
 x 2  y 2  13
35) Solve these systems: 
x  y  1
2 x 2  2 y 2  4 x  6 y  0
 2
2
 x  y  2 x  3 y  1
(Unusual things might
happen)
(6, 7)
No Solution
y
f(x)=-2x^2
8
#2
6
4
2
x
-9
-8
-7
-6
-5
-4
-3
-2
-1
1
-2
-4
-6
-8
2
3
4
5
6
7
8
9
y
#3
f(x)=(x+7)^2+4
8
6
4
2
x
-9
-8
-7
-6
-5
-4
-3
-2
-1
1
-2
-4
-6
-8
2
3
4
5
6
7
8
9
#4
y
f(x)=.5(x+1)^2+3
Shade 1
8
6
4
2
x
-9
-8
-7
-6
-5
-4
-3
-2
-1
1
-2
-4
-6
-8
2
3
4
5
6
7
8
9
#5
y
f(x)=3(x-2)^2-5
Shade 1
8
6
4
2
x
-9
-8
-7
-6
-5
-4
-3
-2
-1
1
-2
-4
-6
-8
2
3
4
5
6
7
8
9